44.6.32 problem 32

Internal problem ID [7176]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 32
Date solved : Tuesday, February 04, 2025 at 12:44:23 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+4 y x&=x^{3} {\mathrm e}^{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 33

dsolve([diff(y(x),x)+4*x*y(x)=x^3*exp(x^2),y(0) = -1],y(x), singsol=all)
 

\[ y = \frac {\left (3 \,{\mathrm e}^{3 x^{2}} x^{2}-{\mathrm e}^{3 x^{2}}-17\right ) {\mathrm e}^{-2 x^{2}}}{18} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 33

DSolve[{D[y[x],x]+4*x*y[x]==x^3*Exp[x^2],{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{18} e^{-2 x^2} \left (e^{3 x^2} \left (3 x^2-1\right )-17\right ) \]